The Modern Difficulty of Tertiary Harmony
and why ChatGPT sucks at it
Publisher’s Reading:
Teaching Chat GPT Music Theory
I’ve spent a considerable amount of time over the past few days trying to teach Chat GPT music theory. It has been very frustrating because it seems to have learned a great deal—it will properly tell you how to build a major scale and the formula involved, etc.— but it seems to be incapable of fully drawing on the data it has (presumably) mastered. Often times, it will just ignore parts of my inquiries, like for example, when I ask it to name a chord from a series of notes—not only will it often get them wildly wrong, not referencing the major scale which I know it knows, but it will often try to name a chord based off of a different set of notes that I didn’t give it. I’ve berated him (Chat GPT becomes a “him” when it’s being scorned) many times and it seems to me that either one, there are wild programming deficiencies still with ChatGPT, or two, music theory is much more complicated than I give it credit.
The Difficulty of Music Theory Nomenclature
Now, naming chords from scale tones is pretty straight forward theoretically—what causes the most confusion, I believe, is the nomenclature. There are a myriad of reasons, but I will simply give one example as it was an instructive moment for me this week. I’m going to be technical, which naturally may go over the non-musician’s head, but I’ll do some explaining to try to illuminate the point.
Chords are typically named from scale tones. For example, the C Major scale (all white notes on the piano) has the notes: C, D, E, F, G, A and B. You can find various common chords by simply stacking notes using these scale tones and skipping a note after each selection. So, C (skip a note), E (skip a note), and G make the chord ‘C major,’ usually abbreviated as “Cmaj.” If you do this and build a three-note chord (triad) starting from each of the various notes of the scale, then you have… nearly every pop song ever written in history. Alternatively, you can continue stacking and have more than three notes in a chord, for example: C, E, G, B, D, F and A, is named a ‘Cmaj13’1. Notice here, I skipped a note every time, so we cycled through the scale twice, into a second octave (an octave, for our purposes here, is where the scale repeats).
Now’s a good time to tell you that we number the scale tones through two octaves, like this: C(1), D(2), E(3), F(4), G(5), A(6), B(7)— the new octave starts—C(1), D(9), E(3), F(11), G(5), A(13), B(7). Okay okay, maybe I’ve been too hard on Chat GPT, but thankfully it can’t have hurt feelings. Of course, I’m being a bit jocular— the second octave can be numbered simply 8-14, so I apologize to anyone who wants to learn theory and I’m just confusing even more. There is, however, much truth to this in practice, even if it would be a little absurd to teach as such to a new music student! Essentially, not every tone in the scale is created equally, especially for chord-building purposes, and certain notes keep their functional-numeric names (1, 3, 5, 7 in particular) regardless of what octave you play them in. For example, going back to that C major chord—the notes C(1), E(3) & G(5)— regardless of where you play the E, it will almost always be called the “3rd” in the chord (being the 3rd note in the scale) and rarely, if ever the 10th! This is the basics of “tertiary harmony” (making chords by stacking 3rds within a scale), but we’ll come back to that term.
Guitar Players are the Problem (Just Kidding!)
At this point, I think I’ve given you plenty to demonstrate that it’s the nomenclature of music theory that can make it difficult. This problem has been exacerbated, I think, by the increased popularity of the guitar over the last one hundred years. While standard music notation is still alive and well in the classical-guitar world; still, the vast majority of guitar players are not well versed in the discipline. This is a topic perhaps worthy of another post entirely. I will only note that the layout of the guitar is less than ideal for standard notation, at least compared to say, the piano, for which it was primarily devised2. The consequence—and I understand this is a broad generalization—is that we use standard notation less, and the numbering system3 way more, but I digress.
Despite Theory’s Vastness, Agreement is Advantageous!
I want to say something briefly about theory, in general. There is a kind of absurdity to music theory, which anyone who plays music will have a feel for, I think. I’m not at all saying that it can’t be helpful or even necessary— it surely is and can be!—but in what way can one even ponder the extent to which knowledge guides movement in a particular moment? And is the bodily movement not a theoretical component in and of itself? Does music theory not encompass the (astronomically dense) topic of the approach of our bodies, fingers and hands in its percussive intents outside of the domain of the note-naming nomenclature? The reason I bring this up is two-fold. One is simply to say that music theory (in its colloquial usage) isn’t the end-all-be-all of making good music. It’s simply a tool! Secondly, it may just be my attempt at pacifying the naysayers of us music theory enthusiasts. Nevertheless, music theory is retrospective more than prescriptive—even if it can be both— and having some general agreement regarding how we refer to certain figures, or theoretical concepts, should be to our advantage, the discontinuity of which, has certainly pushed away some prying minds in the modern era.
Chord Naming with Tertiary Harmony
I was doing some theory-grazing on YouTube in preparation for a project I’ve been working on, when a certain YouTuber mentioned a ‘Cadd2’ chord, and admitted that it was confusing. Now ‘Cadd2’ seems simple enough, we have the aforementioned C Major chord (notes: C, E, & G), and then we add the ‘2,’ or second note in the major scale, which is D. So ‘Cadd2’ would contain the notes C, E, G, & D. I jumped into the comments because I love a good music theory brawl, and found what I was looking for! A fellow music theory nerd—I’ll call him “TheoryDude” for anonymity— appealed to a stricter adherence to the principals of tertiary harmony:
“…Building chords using tertiary harmony is the fundamental method of chord building, not the other way around. When I was first learning theory over 30 years ago, I would have be reprimanded for calling a chord a ‘Cadd2’ or ‘Cadd4,’ because 2, 4, and 6 were never considered chord tones. 1, 3, 5, 7, 9, 11, and 13 were chord tones and 2, 4, and 6 were specifically reserved for suspensions… Voicing should have no bearing on what you call a given chord tone, because all of those values are set by the theoretical chord, built from first principles using tertiary harmony. So what I'm saying is that whether you put a D a 2nd away from your C root or an actual 9th away, or literally anywhere else, if you are claiming that C is your root, then D is the 9th, period. The actual interval away from the root of something is not the same as its pitch function in the chord. This is why 6/9 chords break my brain. To me, that sounds like using two different incompatible units of measurement, like telling you that l'm 5 feet and 7 gallons tall. That makes no sense. I don't know when or where this started, and it's almost assuredly born out of jazz nomenclature, but this is not how I learned chord building, and I'm glad, because it is unnecessarily complicated and confusing.”
He makes a great point, honestly, and it is confusing that it’s simply a matter of preference, in the modern era, whether you call call this chord a ‘Cadd2’ or ‘Cadd9.’ Technically speaking, he’s right, and it should always be called ‘Cadd9,’ if we agree that tertiary harmony is the fundamental way we name chords. But there are two schools of thought! One school of thought—that TheoryDude is promulgating—is that the voicing (i.e. in what order and in what octave the notes are played) should not influence the name of the chord. So, as TheoryDude mentioned, whether the ‘D’ note is a whole step above the root (C), or seven whole-steps and in the next octave, it should be called ‘Cadd9’ either way. Of course, the contrary school of thought is that in the former case it should be called ‘Cadd2,’ and if the D is in the next octave, then ‘Cadd9.’ While this might be helpful in some situations, it sort of belies the hopelessness of chord naming in general to mandate a musical passage like standard notation can. The piano, with its seven octave span, brings this to light. Shall we call it a ‘Cadd16,’ or ‘Cadd30’ if the D comes two octave later? Nonsense. Practicality wins the day here and I agree with TheoryDude’s general conclusion.
There is some subtlety in the usage of scale degrees 2 & 4, as in suspended chords, or “sus” chords for short (e.g. ‘Csus2’ or ‘Csus4’ or, colloquially, ‘Csus’). Suspended chords are characterized by the 3rd of the chord being omitted and replaced by scale degree 2 or 4. For example, a ‘Csus4’ chord, common in rock & pop music, has the notes C(1), F(4), and G(5). The 3rd (E) has been ‘suspended’ to F and frequently, though certainly not always, resolves back to an E. This, again, goes to TheoryDude’s point that “voicing should have no bearing on what you call a given chord.” Function is what matters! Anybody who hears a Csus resolve to Cmaj will immediately understand the intuitive relationship. The resolution will, in most cases, happen within the same octave, but that is not why we’re naming the chord ‘sus4’ as opposed to ‘sus11’; rather, it's the 4ths functional relationship, as existing a semi-tone from the 3rd. Now, I know this may seem very pedantic, unless you love theory or teach it for a living, but again, my goal here is to try to bring some continuity to the subject, where it certainly has been lacking. I never had a huge problem myself with seeing a ‘Cadd2’ chord (or, worse, ‘C2’) but going forward, I think it’s reasonable to insist, with the presence of the 3rd, they, minding theoretical principals, technically should be called “add9” chords.
You might recall TheoryDude included the 6th scale degree in referencing suspended chords, and while I think it can be heard as such—the 6 resolving to 5—theoretically speaking, this is superfluous, as it forms a minor chord. For example, what might be called ‘Csus6’— the notes C(1), E(3) & A(6)— is simply a second inversion A minor (Am). Perhaps some consider a ‘Csus6’ to contain the notes C, F, & A—with a suspended 4th—but again, that is simply a second inversion F Major chord. In a nutshell, ‘sus6’ is redundant and unnecessary. If you disagree, please share your thoughts in the comments.
Lastly, I want to defend the “6/9” chord. While I understand TheoryDude’s hangup with it, and perhaps it’s a little at odds with my previous support of his main idea, surely we can let jazz nomenclature spot us this little jewel… this little outlier. I don’t know why I have a much harder time parting with the 6/9 chord. For those of you who don’t know, but want to know, a 6/9 chord is a chord, either major or minor, that includes the 6th and 9th scale tones. So for example, ‘C6/9’ would comprise the notes C(1), E(3), G(5), A(6) & D(9); Cm6/9 would have the minor 3rd— C(1), Eb(b3), G(5), A(6) & D(9). Of course, if we were sticking strictly to tertiary harmony, technically speaking it should be called C(add9add13) or C(9,13), with a 13 as opposed to a 6. My main argument is simply the spoken and written aesthetic: “Nine/thirteen” is clunky compared to “six/nine” in both cases. So… sorry TheoryDude, we are formally adopting the “6/9” chord, lest we be accused by theory naysayers of being inflexible!
At the end of the day, I’m not holding my breathe that we’re going to magically come to some grand agreement on these matters. Nevertheless, the discussion ought to continue in earnest, for our mutual enjoyment and edification, as we learn to appreciate the different approaches, settle our differences… and err, tip our hat to anyone who is trying to learn music theory from Chat GPT!
Of course, in practice, some notes would be omitted to taste, but this is a theoretical post.
Or its precursors (clavichord, etc.)
Colloquially known today as the “Nashville Numbering System,” no doubt because of the efficacy of the system and its role in modern songwriting exploits.